Sarah Fabian, an attorney for the Justice Department, said of that group, about half of the children have parents in custody of Immigration and Customs Enforcement, and for that group, the reunification can occur by the deadline.
"This isn't some vast sprawling data set that we're matching up", he said.
On Thursday, Health and Human Services Secretary Alex Azar said fewer than 3,000 children are believed to have been separated, but that includes kids who may have lost parents along the journey, not just parents who were detained at the border.
Still, the more than 2,000 children who were separated already are proving to be hard for the administration to grapple with.
The government's court documents describe an extensive and painstaking effort to collect information between the Departments of Homeland Security and Health and Human Services; verify the parentage; and assess the parents' "fitness" to receive their children.
The US government has asked for more time to reunite migrant families separated at the US-Mexico border as it emerged that some children's parents have already been deported.
In his comments on Thursday, Azar said that "under 3,000" minors were separated from their parents. That deadline in some cases doesn't give authorities enough time to ensure children are returned to.
Lawyers for the agency argue that meeting an upcoming July 10 court-mandated deadline to reunite children under age 5 and a subsequent deadline to reunite the almost 3,000 remaining children later this month would be hard.
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Mr Azar said that in order to comply with the deadline, normal vetting processes may need to be abandoned.
The organization said they'd never heard of DNA testing being done to reunite families before and they don't support the move.
The judge, who has yet to rule on the extension, said the government needed to provide a full list of those under five held in custody by Saturday afternoon, following which the original deadline would be re-evaluated. "To our knowledge, this is a cheek swab and is being done to expedite parental verification and ensuring reunification with verified parents due to child welfare concerns", one official told CNN. While the court's order included no dates and covers all families who were separated by the Trump administration, the Justice Department is requesting that only those separated after March 9 be counted - the date the class action lawsuit was filed.
Officials have said they'll comply with the judge's order, but they haven't specified what steps they'll take to do that.
Only about 101 children under age five are in the care of Office of Refugee Resettlement, according to the government.
Government officials feel aggrieved in general at the stress caused by their practice, now halted, of separating parents and children in enforcing misdemeanor border-crossing crimes.
The department has manually reviewed the cases of all 11,800 children in its custody by working nights and weekends, White said.